library(readr)
library(ggplot2)
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2
## ──
## ✔ tibble 3.1.8 ✔ stringr 1.5.0
## ✔ tidyr 1.3.0 ✔ forcats 1.0.0
## ✔ purrr 1.0.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
library(grid)
library(cowplot)
library(factoextra)
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library(corrplot)
## corrplot 0.92 loaded
library(devtools)
## Loading required package: usethis
library(FactoMineR)
library(ggfortify)
library(psych)
##
## Attaching package: 'psych'
##
## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha
library(vctrs)
##
## Attaching package: 'vctrs'
##
## The following object is masked from 'package:tibble':
##
## data_frame
##
## The following object is masked from 'package:dplyr':
##
## data_frame
library(purrr)
library("corrplot")
tita <- read_csv("/Users/asrithanarra/Documents/Multivariate analysis/Titanic.csv")
## Rows: 891 Columns: 5
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Survived
## dbl (4): PassengerId, Pclass, Age, Fare
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
str(tita)
## spc_tbl_ [891 × 5] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Survived : chr [1:891] "No" "yes" "yes" "yes" ...
## $ PassengerId: num [1:891] 1 2 3 4 5 6 7 8 9 10 ...
## $ Pclass : num [1:891] 3 1 3 1 3 3 1 3 3 2 ...
## $ Age : num [1:891] 22 38 26 35 35 10 54 2 27 14 ...
## $ Fare : num [1:891] 7.25 71.28 7.92 53.1 8.05 ...
## - attr(*, "spec")=
## .. cols(
## .. Survived = col_character(),
## .. PassengerId = col_double(),
## .. Pclass = col_double(),
## .. Age = col_double(),
## .. Fare = col_double()
## .. )
## - attr(*, "problems")=<externalptr>
attach(tita)
summary(tita)
## Survived PassengerId Pclass Age
## Length:891 Min. : 1.0 Min. :1.000 Min. : 1.00
## Class :character 1st Qu.:223.5 1st Qu.:2.000 1st Qu.:22.00
## Mode :character Median :446.0 Median :3.000 Median :28.00
## Mean :446.0 Mean :2.309 Mean :30.32
## 3rd Qu.:668.5 3rd Qu.:3.000 3rd Qu.:38.00
## Max. :891.0 Max. :3.000 Max. :92.00
## Fare
## Min. : 0.000
## 1st Qu.: 7.925
## Median : 15.100
## Mean : 33.389
## 3rd Qu.: 31.275
## Max. :512.329
cor(tita[-1])
## PassengerId Pclass Age Fare
## PassengerId 1.0000000000 -0.03514399 0.04815802 0.0008510998
## Pclass -0.0351439940 1.00000000 -0.30758636 -0.5431017648
## Age 0.0481580247 -0.30758636 1.00000000 0.0842967291
## Fare 0.0008510998 -0.54310176 0.08429673 1.0000000000
plot(tita[,-1])
library(GGally)
## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2
ggpairs(tita[,c( "Survived","PassengerId", "Pclass", "Age","Fare")],aes(color = factor(Survived)))
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
p1 <- ggplot(tita, aes(x=PassengerId, y=Pclass, color=Survived)) + geom_point()
p2 <- ggplot(tita, aes(x=Age, y=Fare, color=Survived)) + geom_point()
p3 <- ggplot(tita, aes(x=Age, y=PassengerId, color=Survived)) + geom_point()
p4 <- ggplot(tita, aes(x=Pclass, y=Fare, color=Survived)) + geom_point()
plot_grid(p1, p2, p3, p4, labels = "AUTO")
tita_pca <- prcomp(tita[,-1],scale=TRUE)
tita_pca
## Standard deviations (1, .., p=4):
## [1] 1.2905711 1.0074002 0.9542240 0.6395527
##
## Rotation (n x k) = (4 x 4):
## PC1 PC2 PC3 PC4
## PassengerId 0.06565727 -0.90999815 -0.40894567 0.01886594
## Pclass -0.68367669 -0.05910479 0.05521554 0.72528894
## Age 0.39775028 -0.32819164 0.80738894 0.28671950
## Fare 0.60833381 0.24637418 -0.42170818 0.62561326
summary(tita_pca)
## Importance of components:
## PC1 PC2 PC3 PC4
## Standard deviation 1.2906 1.0074 0.9542 0.6396
## Proportion of Variance 0.4164 0.2537 0.2276 0.1023
## Cumulative Proportion 0.4164 0.6701 0.8977 1.0000
plot(tita_pca)
tita_pca
## Standard deviations (1, .., p=4):
## [1] 1.2905711 1.0074002 0.9542240 0.6395527
##
## Rotation (n x k) = (4 x 4):
## PC1 PC2 PC3 PC4
## PassengerId 0.06565727 -0.90999815 -0.40894567 0.01886594
## Pclass -0.68367669 -0.05910479 0.05521554 0.72528894
## Age 0.39775028 -0.32819164 0.80738894 0.28671950
## Fare 0.60833381 0.24637418 -0.42170818 0.62561326
(eigen_tita <- tita_pca$sdev^2)
## [1] 1.6655736 1.0148552 0.9105435 0.4090277
names(eigen_tita) <- paste("PC",1:4,sep="")
eigen_tita
## PC1 PC2 PC3 PC4
## 1.6655736 1.0148552 0.9105435 0.4090277
sumlabdas<-sum(eigen_tita)
sumlabdas
## [1] 4
propvar<-eigen_tita/sumlabdas
propvar
## PC1 PC2 PC3 PC4
## 0.4163934 0.2537138 0.2276359 0.1022569
cumvar<-cumsum(propvar)
cumvar
## PC1 PC2 PC3 PC4
## 0.4163934 0.6701072 0.8977431 1.0000000
matlambdas <- rbind(eigen_tita,propvar,cumvar)
rownames(matlambdas) <- c("Eigenvalues","Prop. variance","Cum. prop. variance")
round(matlambdas,4)
## PC1 PC2 PC3 PC4
## Eigenvalues 1.6656 1.0149 0.9105 0.4090
## Prop. variance 0.4164 0.2537 0.2276 0.1023
## Cum. prop. variance 0.4164 0.6701 0.8977 1.0000
summary(tita_pca)
## Importance of components:
## PC1 PC2 PC3 PC4
## Standard deviation 1.2906 1.0074 0.9542 0.6396
## Proportion of Variance 0.4164 0.2537 0.2276 0.1023
## Cumulative Proportion 0.4164 0.6701 0.8977 1.0000
tita_pca$rotation
## PC1 PC2 PC3 PC4
## PassengerId 0.06565727 -0.90999815 -0.40894567 0.01886594
## Pclass -0.68367669 -0.05910479 0.05521554 0.72528894
## Age 0.39775028 -0.32819164 0.80738894 0.28671950
## Fare 0.60833381 0.24637418 -0.42170818 0.62561326
tita_pca$x
## PC1 PC2 PC3 PC4
## [1,] -1.224789952 1.591832e+00 0.493032238 0.0777818918
## [2,] 1.625007860 1.666786e+00 0.745451365 -0.5472209837
## [3,] -1.103520752 1.495017e+00 0.713072412 0.1674523980
## [4,] 1.324249082 1.641688e+00 0.720920576 -0.8309019381
## [5,] -0.847915525 1.279294e+00 1.223651608 0.3519432306
## [6,] -1.547252191 1.858991e+00 -0.211283668 -0.1507895692
## [7,] 1.845652645 1.183347e+00 1.813157746 -0.4599148610
## [8,] -1.621785174 2.098829e+00 -0.776301561 -0.1584874252
## [9,] -1.035570658 1.466038e+00 0.734227701 0.2275319110
## [10,] -0.358184922 1.926870e+00 -0.233464501 -0.6718178975
## [11,] -1.616810493 2.020600e+00 -0.630521362 -0.1712712149
## [12,] 1.657931836 9.504729e-01 2.243158923 -0.6885782840
## [13,] -1.268549617 1.599763e+00 0.352955750 0.0478430692
## [14,] -0.456078004 1.266583e+00 1.246243564 0.7185439870
## [15,] -1.439443222 1.731249e+00 0.008202102 -0.0762850737
## [16,] 0.630942254 8.844586e-01 2.218419701 -0.0110473235
## [17,] -1.523537891 2.105865e+00 -0.857118035 -0.0591510449
## [18,] -0.334190889 1.630171e+00 0.352466086 -0.7179851672
## [19,] -0.838459118 1.370824e+00 0.890395104 0.3936865149
## [20,] -1.220240572 1.524528e+00 0.463047037 0.0788682829
## [21,] 0.187845082 1.380062e+00 0.983868989 -0.2943499693
## [22,] 0.004969680 1.337021e+00 1.032496751 -0.4739426413
## [23,] -1.407137992 1.680556e+00 0.051242699 -0.0532410295
## [24,] 0.922321774 1.648761e+00 0.434171789 -1.1873630545
## [25,] -1.448378021 1.899214e+00 -0.460121836 -0.0353665516
## [26,] -0.479853916 1.247945e+00 1.169046617 0.7004902552
## [27,] -1.218454700 1.499776e+00 0.451923754 0.0793814346
## [28,] 3.381400508 2.942091e+00 -1.966749325 1.4188051166
## [29,] -1.210146780 1.495862e+00 0.443340184 0.0875472097
## [30,] -1.181515454 1.469156e+00 0.498812884 0.1081364407
## [31,] 1.169524327 1.307450e+00 1.173712890 -1.0384577635
## [32,] 2.106772294 2.272660e+00 -0.781871774 0.0725502181
## [33,] -1.182487929 1.457844e+00 0.495250471 0.1065691516
## [34,] 0.879939532 5.385050e-01 2.864450003 0.1462902599
## [35,] 1.481416034 1.835161e+00 0.031063354 -0.6144676657
## [36,] 1.516550102 1.360473e+00 1.079552617 -0.6998527733
## [37,] -1.215853393 1.464437e+00 0.435998645 0.0801659919
## [38,] -1.233993165 1.488113e+00 0.370428640 0.0699881951
## [39,] -1.199675038 1.602361e+00 0.115028565 0.1310909247
## [40,] -1.392688145 1.659202e+00 -0.059513964 -0.0329285345
## [41,] -0.680854202 1.042625e+00 1.440666248 0.4736121025
## [42,] -0.091821012 1.467674e+00 0.534221654 -0.5165998675
## [43,] -1.178198836 1.423188e+00 0.478155358 0.1090894366
## [44,] -0.522299208 2.117957e+00 -1.011770794 -0.7516927434
## [45,] -1.290599806 1.509038e+00 0.246318830 0.0277828037
## [46,] -1.175595491 1.413325e+00 0.472114121 0.1111995369
## [47,] -0.522974058 9.807421e-01 1.552945664 0.6088435068
## [48,] -0.868699330 1.149049e+00 1.100602789 0.3311056173
## [49,] -0.730594851 1.236004e+00 0.926721397 0.4816101218
## [50,] -1.199252548 1.562500e+00 0.099201669 0.1294457130
## [51,] -1.248073308 1.920378e+00 -0.712426160 0.1743783624
## [52,] -1.233401272 1.437403e+00 0.350247760 0.0679500073
## [53,] 2.012892797 1.256984e+00 1.248600133 -0.2532898036
## [54,] 0.027194156 1.402878e+00 0.588237240 -0.4138054740
## [55,] 2.288445338 8.067009e-01 2.282479999 -0.1089491027
## [56,] 1.099555794 1.396107e+00 0.726515907 -1.0631425701
## [57,] -0.382217871 1.503450e+00 0.253951471 -0.7660835318
## [58,] -1.041425743 1.250678e+00 0.745822209 0.2035800951
## [59,] -0.626951416 1.951658e+00 -0.806941423 -0.8794860920
## [60,] -1.047095165 1.830369e+00 -0.557526975 0.3446984630
## [61,] -1.209730405 1.379573e+00 0.397861674 0.0819253690
## [62,] 1.744213156 1.496705e+00 0.578085053 -0.4359735420
## [63,] 1.983136567 1.347191e+00 0.948175284 -0.2511167186
## [64,] -1.469791624 1.887259e+00 -0.807283268 -0.0300967217
## [65,] 0.699166793 1.582485e+00 0.147304176 -1.3812768158
## [66,] -1.084723389 1.377342e+00 0.380876240 0.2008715451
## [67,] -0.154239911 1.282086e+00 0.695652284 -0.6028509271
## [68,] -1.281405238 1.429058e+00 0.207464766 0.0328900714
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## [76,] -1.116352837 1.258813e+00 0.542145810 0.1491204553
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## [79,] 1.590960785 7.343304e-02 3.612463709 0.7216729377
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## [83,] -0.887501334 1.048721e+00 0.987477617 0.3138186080
## [84,] 1.075894274 1.492599e+00 0.242981501 -1.0407722239
## [85,] 0.847184955 2.038107e+00 -0.944764881 0.5276113285
## [86,] -0.790635805 1.077034e+00 0.916092101 0.4128683685
## [87,] -1.048605580 1.558183e+00 -0.210945656 0.2947089643
## [88,] -0.571049242 7.773975e-01 1.605105387 0.5429848593
## [89,] 3.509676460 2.633394e+00 -1.834885186 1.5045266323
## [90,] -1.134105778 1.235336e+00 0.457949261 0.1368826468
## [91,] -0.992958958 1.115547e+00 0.742354732 0.2385181610
## [92,] -1.250728599 1.319476e+00 0.229039398 0.0512342429
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## [94,] 1.478194590 2.209430e+00 -1.205128811 2.8052954403
## [95,] -0.158209696 3.991814e-01 2.460021815 0.8362331162
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## [97,] 2.142533023 3.867797e-01 2.784713261 -0.3189444233
## [98,] 1.132363486 1.637832e+00 -0.199597789 -0.9420144639
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## [105,] -0.767536320 8.785912e-01 1.180178207 0.3983666059
## [106,] -1.021234295 1.084169e+00 0.664040319 0.2152700085
## [107,] -1.221157334 1.242200e+00 0.264089946 0.0701432186
## [108,] -1.163055606 1.192766e+00 0.375865867 0.1123736543
## [109,] -0.738685529 8.410558e-01 1.231262220 0.4186143443
## [110,] -0.967365197 1.264742e+00 0.237385311 0.3132444370
## [111,] 1.676576137 9.790221e-01 1.246369092 -0.5927925128
## [112,] -1.336028111 1.420120e+00 -0.200468952 0.0117283077
## [113,] -1.184594593 1.200509e+00 0.307003526 0.0979438338
## [114,] -1.221625109 1.251198e+00 0.177796287 0.0770050016
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## [116,] -1.215583379 1.211704e+00 0.247516326 0.0741739253
## [117,] 0.163324475 6.804797e-02 3.050119476 1.0674117158
## [118,] -0.016074871 1.152438e+00 0.527852382 -0.4704036238
## [119,] 3.361023413 2.429348e+00 -1.697469021 1.3373129535
## [120,] -1.471633358 1.752038e+00 -1.038554109 -0.0252457611
## [121,] 0.385032240 1.581270e+00 -0.368300150 0.0108599013
## [122,] -1.154120133 1.145435e+00 0.349901064 0.1189160416
## [123,] 3.660183311 2.519132e+00 -1.797460342 3.2833328913
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## [155,] -1.156577476 1.024343e+00 0.305002484 0.1101497926
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## [708,] 1.381516224 -1.139829e+00 0.224173284 -0.9657731242
## [709,] 2.311258290 -7.367015e-02 -1.956406086 0.1635146286
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## [722,] -1.184070695 -8.423022e-01 -0.937042614 0.0266741973
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## [730,] -0.946223572 -1.052390e+00 -0.499358920 0.2004344227
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## [738,] 6.985246573 1.263133e+00 -4.239929609 4.8521208906
## [739,] -0.972453838 -1.061105e+00 -0.570617914 0.1804238152
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## [743,] 3.612721586 3.643466e-01 -2.983351248 1.5041835490
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## [745,] -0.773326669 -1.244933e+00 -0.180001113 0.3234086817
## [746,] 2.713150586 -1.709368e+00 1.395910955 0.1538451502
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## [780,] 3.633748327 -5.243710e-01 -1.362059971 1.3281537712
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## [817,] -0.980384419 -1.313520e+00 -0.752003246 0.1661872822
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## [832,] 1.660895701 -2.638640e+00 2.500609379 0.6512292600
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## [834,] -0.976891195 -1.373973e+00 -0.778431932 0.1665656438
## [835,] -1.112214099 -1.259105e+00 -1.069699016 0.0705413449
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## [839,] 0.505869925 -1.900860e+00 0.642074527 1.4131773083
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## [843,] 1.133988130 -1.315431e+00 -0.715672201 -1.1418602667
## [844,] -0.681264431 -1.671927e+00 -0.153428579 0.3733697144
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## [847,] 0.015407338 -1.331369e+00 -0.794076094 1.1065955355
## [848,] -0.634683534 -1.702282e+00 -0.114635402 0.4118511748
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## [850,] 1.574736096 -8.504398e-01 -1.721685880 -0.6119198689
## [851,] -1.228780663 -8.792652e-01 -2.085744896 0.0689668172
## [852,] 0.463852331 -2.623779e+00 2.110763763 1.2028488555
## [853,] -1.278437149 -1.079968e+00 -1.670483249 -0.0258097250
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## [856,] -1.094341115 -1.328292e+00 -1.111744750 0.0849516626
## [857,] 3.155845582 -1.067473e+00 -0.986041843 0.8047859077
## [858,] 1.676518796 -1.878213e+00 0.498438361 -0.7687473291
## [859,] -0.806404724 -1.430572e+00 -0.855188229 0.3285018221
## [860,] -1.315847654 -1.189920e+00 -1.500969594 -0.0829388885
## [861,] -0.388247613 -1.857763e+00 0.156568173 0.6108314231
## [862,] -0.164923241 -1.338187e+00 -1.033488862 -0.6948131255
## [863,] 1.585859838 -1.829138e+00 0.324025965 -0.8369278606
## [864,] -0.543822331 -9.264707e-01 -1.965067827 0.7015929337
## [865,] -0.061743751 -1.411305e+00 -0.879053396 -0.6152689326
## [866,] 0.445721480 -1.833350e+00 0.148937804 -0.2495716807
## [867,] 0.033531936 -1.483985e+00 -0.717726686 -0.5436639829
## [868,] 1.400922802 -1.332968e+00 -0.859288164 -0.8807363173
## [869,] -1.230128283 -1.257283e+00 -1.419636199 -0.0138188536
## [870,] -1.464010257 -1.043680e+00 -1.949510904 -0.1765365852
## [871,] -0.882420724 -1.574355e+00 -0.665973453 0.2307252723
## [872,] 1.877331620 -1.709184e+00 0.032530073 -0.5302122319
## [873,] 0.916272507 -1.616773e+00 -0.376915299 -1.3974307970
## [874,] -0.276748825 -2.067893e+00 0.521312648 0.6710417075
## [875,] 0.184634241 -1.486566e+00 -0.757038404 -0.3984484843
## [876,] -1.199102366 -1.339518e+00 -1.297563930 -0.0005676884
## [877,] -1.026717184 -1.446655e+00 -1.034813465 0.1331934991
## [878,] -1.077883227 -1.436354e+00 -1.077489052 0.0890513344
## [879,] -1.246698138 -1.300386e+00 -1.422271506 -0.0327500064
## [880,] 2.497760150 -1.798990e+00 0.281733948 0.0283301695
## [881,] 0.125468768 -1.428376e+00 -0.954694846 -0.4344300352
## [882,] -0.682365979 -1.776005e+00 -0.283060583 0.3737187430
## [883,] -0.960833034 -1.511133e+00 -0.935493380 0.1824820944
## [884,] 0.026018474 -1.583559e+00 -0.659792690 -0.5632712381
## [885,] -0.917108748 -1.604691e+00 -0.738430291 0.2010713479
## [886,] -0.259236139 -1.827171e+00 -0.121634829 0.7561133998
## [887,] 0.028404006 -1.558848e+00 -0.742415580 -0.5527188461
## [888,] 0.823587602 -1.223622e+00 -1.408104200 -1.3742562540
## [889,] -1.058750176 -1.260661e+00 -1.566682323 0.1586458981
## [890,] 1.021346226 -1.393447e+00 -1.010889966 -1.2319225497
## [891,] -0.709986046 -1.785282e+00 -0.353356141 0.3522788569
var <- get_pca_var(tita_pca)
var
## Principal Component Analysis Results for variables
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the variables"
## 2 "$cor" "Correlations between variables and dimensions"
## 3 "$cos2" "Cos2 for the variables"
## 4 "$contrib" "contributions of the variables"
plot(eigen_tita, xlab = "Component number", ylab = "Component variance", type = "l", main = "Scree diagram")
pairs.panels(tita[-1],
gap = 0,
bg = c("red", "blue")[tita$Survived],
pch=21)
diag(cov(tita_pca$x))
## PC1 PC2 PC3 PC4
## 1.6655736 1.0148552 0.9105435 0.4090277
xlim <- range(tita_pca$x[,1])
plot(tita_pca$x,xlim=xlim,ylim=xlim)
#Correlation circle
head(var$coord, 4)
## Dim.1 Dim.2 Dim.3 Dim.4
## PassengerId 0.08473538 -0.91673233 -0.3902258 0.01206576
## Pclass -0.88233335 -0.05954218 0.0526880 0.46386051
## Age 0.51332500 -0.33062032 0.7704299 0.18337223
## Fare 0.78509800 0.24819741 -0.4024041 0.40011266
fviz_eig(tita_pca, addlabels = TRUE)
fviz_pca_var(tita_pca,col.var = "cos2",
gradient.cols = c("#FFCC00", "#CC9933", "#660033", "#330033"),
repel = TRUE)
biplot(tita_pca)
head(var$cos2, 4)
## Dim.1 Dim.2 Dim.3 Dim.4
## PassengerId 0.007180084 0.840398167 0.152276167 0.0001455826
## Pclass 0.778512135 0.003545271 0.002776025 0.2151665693
## Age 0.263502553 0.109309798 0.593562274 0.0336253747
## Fare 0.616378869 0.061601952 0.161929040 0.1600901383
corrplot(var$cos2, is.corr=FALSE)
fviz_pca_var(tita_pca, col.var = "cos2",
gradient.cols = c("#00FF00", "#FF0000", "#FC4E07"),
repel = TRUE
)
#Contributions of Pc
head(var$contrib, 4)
## Dim.1 Dim.2 Dim.3 Dim.4
## PassengerId 0.4310877 82.8096636 16.7236563 0.03559235
## Pclass 46.7413818 0.3493376 0.3048756 52.60440497
## Age 15.8205285 10.7709750 65.1876896 8.22080696
## Fare 37.0070019 6.0700239 17.7837785 39.13919571
corrplot(var$contrib, is.corr=FALSE)
fviz_pca_var(tita_pca, col.var = "contrib",
gradient.cols = c("#00FF00", "#E7B800", "#FC4E07")
)
# Contributions of PC1
fviz_contrib(tita_pca, choice = "var", axes = 1, top = 10)
# Contributions of PC2
fviz_contrib(tita_pca, choice = "var", axes = 2, top = 10)
fviz_contrib(tita_pca, choice = "var", axes = 1:2, top = 10)
#Graphs of ind
ind <- get_pca_ind(tita_pca)
ind
## Principal Component Analysis Results for individuals
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the individuals"
## 2 "$cos2" "Cos2 for the individuals"
## 3 "$contrib" "contributions of the individuals"
# Coordinates of individuals
head(ind$coord)
## Dim.1 Dim.2 Dim.3 Dim.4
## 1 -1.2247900 1.591832 0.4930322 0.07778189
## 2 1.6250079 1.666786 0.7454514 -0.54722098
## 3 -1.1035208 1.495017 0.7130724 0.16745240
## 4 1.3242491 1.641688 0.7209206 -0.83090194
## 5 -0.8479155 1.279294 1.2236516 0.35194323
## 6 -1.5472522 1.858991 -0.2112837 -0.15078957
# Quality of individuals
head(ind$cos2)
## Dim.1 Dim.2 Dim.3 Dim.4
## 1 0.3502336 0.5916014 0.056752524 0.001412510
## 2 0.4208897 0.4428094 0.088571904 0.047729055
## 3 0.3052526 0.5602611 0.127457556 0.007028798
## 4 0.3098898 0.4762657 0.091842312 0.122002158
## 5 0.1807915 0.4115412 0.376520245 0.031147127
## 6 0.4045803 0.5840329 0.007544221 0.003842600
# Contributions of individuals
head(ind$contrib)
## Dim.1 Dim.2 Dim.3 Dim.4
## 1 0.10108383 0.2802289 0.029962099 0.001660071
## 2 0.17793828 0.3072399 0.068495213 0.082166559
## 3 0.08205772 0.2471783 0.062674209 0.007694003
## 4 0.11816744 0.2980572 0.064061402 0.189438897
## 5 0.04844664 0.1809917 0.184559823 0.033987158
## 6 0.16131720 0.3821844 0.005502416 0.006238960
fviz_pca_ind(tita_pca, col.ind = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping (slow if many points)
)
fviz_pca_ind(tita_pca,
geom.ind = "point",
col.ind = tita$Survived, # color by groups
palette = c("#00FF00", "#E7B800", "#FC4E07"),
addEllipses = TRUE, # ellipses
legend.title = "Survivorship"
)
ind.p <- fviz_pca_ind(tita_pca, geom = "point", col.ind = tita$Survived)
ggpubr::ggpar(ind.p,
title = "Principal Component Analysis",
subtitle = "titanic",
xlab = "PC1", ylab = "PC2",
legend.title = "Survivorship", legend.position = "top",
ggtheme = theme_gray(), palette = "jco"
)
#anova testing
tita_anova <- aov(PassengerId+Pclass ~ Survived, data = tita)
summary(tita_anova)
## Df Sum Sq Mean Sq F value Pr(>F)
## Survived 1 2198 2198 0.033 0.856
## Residuals 889 58930554 66289